To transform the equation \(-10x + 13 + 12x = 5x - 8\) into the form \(x = a\), you can perform a series of algebraic steps. The first step is to simplify the equation by combining like terms on both sides.
Let's analyze the options provided:
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Subtract 10x from both sides of the equation and then simplify.
- This option is useful because it simplifies the left side of the equation. Doing this would lead to combining \(-10x\) and \(12x\), which simplifies the equation.
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Subtract 13 from both sides of the equation and then simplify.
- This option would help isolate terms and simplify the equation further down the line.
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Combine like terms \(10x\) and \(12x\) to get \(22x\), and then subtract \(22x\) from both sides of the equation.
- This is an incorrect step; we cannot add \(10x\) and \(12x\) directly since one is negative. So, this option doesn't apply.
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Add \(5x\) to both sides of the equation and then simplify.
- This option could potentially help in isolating \(x\), but it is not the most efficient first step because we already have a \(5x\) on the right side.
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Add \(8\) to both sides of the equation and then simplify.
- This step would help isolate terms but would come after simplifying or solving the \(x\) terms.
Based on the evaluation, the most logical first steps to transform the equation to the form \(x = a\) are:
- Subtract 10x from both sides of the equation and then simplify. (Option 1)
- Subtract 13 from both sides of the equation and then simplify. (Option 2)
Therefore, the two options that apply are:
- Subtract 10x from both sides of the equation and then simplify.
- Subtract 13 from both sides of the equation and then simplify.